Apparatus and method for capturing still images and video using coded lens imaging techniques

ABSTRACT

An apparatus for capturing images. In one embodiment, the apparatus comprises: a coded lens array including a plurality of lenses arranged in a coded pattern and with opaque material blocking array elements that do not contain lenses; and a light-sensitive semiconductor sensor coupled to the coded lens array and positioned at a specified distance behind the coded lens array, the light-sensitive sensor configured to sense light transmitted through the lenses in the coded lens array.

PRIORITY CLAIM

This application is a continuation-in-part of U.S. patent applicationSer. No. 13/226,461, filed on Sep. 6, 2011, which is a continuation ofU.S. patent application Ser. No. 12/691,500, filed Jan. 21, 2010, nowU.S. Pat. No. 8,013,285, Issued on Sep. 6, 2011, which is a continuationof Continuation-in-Part U.S. patent application Ser. No. 11/210,098entitled “Apparatus And Method For Capturing Still Images And VideoUsing Coded Lens Imaging Technique” filed on Aug. 22, 2005, now U.S.Pat. No. 7,671,321, Issued on Mar. 2, 2010 and claims the benefit ofU.S. patent application Ser. No. 11/039,029, entitled, “Apparatus AndMethod For Capturing Still Images And Video Using Coded ApertureTechniques” filed on Jan. 18, 2005, now U.S. Pat. No. 7,767,949, Issuedon Aug. 3, 2010 and claims the benefit of U.S. Provisional ApplicationNo. 60/701,435 entitled, “Apparatus And Method For Capturing StillImages And Video Using Coded Lens Imaging Techniques”, filed on Jul. 20,2005. This application is incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to the field of image capture and imageprocessing. More particularly, the invention relates to an apparatus andmethod for capturing still images and video using coded lens techniques.

2. Description of the Related Art

Photographic imaging is commonly done by focusing the light coming froma scene using a single glass lens which is placed in front of a lightsensitive detector such as a photographic film or a semiconductor sensorincluding CCD and CMOS sensors.

For imaging high-energy radiation such as x-ray or gamma rays, othertechniques must be used because such radiation cannot be diffractedusing glass lenses. A number of techniques have been proposed includingsingle pinhole cameras and multi-hole collimator systems. A particularlybeneficial technique is “coded aperture imaging” wherein a structuredaperture, consisting of a suitably-chosen pattern of transparent andopaque elements, is placed in front of a detector sensitive to theradiation to be imaged. When the aperture pattern is suitably chosen,the imaged scene can be digitally reconstructed from the detectorsignal. Coded aperture imaging has the advantage of combining highspatial resolution with high light efficiency. Coded aperture imaging ofx-ray and gamma ray radiation using structured arrays of rectangular orhexagonal elements is known from R. H. DICKE: SCATTER-HOLE CAMERA FORX-RAYS AND GAMMA RAYS. ASTROHYS. J., 153:L101-L106, 1968 (hereinafter“Dicke”), and has been extensively applied in astronomical imaging andnuclear medicine.

A particularly useful class of coded imaging systems is known from E. E.FENIMORE AND T. M. C ANNON: CODED APERTURE IMAGING WITH UNIFORMLYREDUNDANT ARRAYS. APPL. OPT., 17:337-347, 1978 (hereinafter “Fenimore”).In this class of systems, a basic aperture pattern is cyclicallyrepeated such that the aperture pattern is a 2×2 mosaic of the basicpattern. The detector has at least the same size as the basic aperturepattern. In such a system, the “fully coded FOV” (“FOV” shall be usedherein to refer to “field-of-view”) is defined as the area within theFOV, within which a point source would cast a complete shadow of acyclically shifted version of the basic aperture pattern onto theaperture. Likewise, the “partially coded FOV” is defined as the areawithin the FOV, within which a point source would only cast a partialshadow of the basic aperture pattern onto the aperture. According toDicke, a collimator is placed in front of the detector which limits theFOV to the fully coded FOV, thus allowing an unambiguous reconstructionof the scene from the detector signal.

From J. GUNSON AND B. POLYCHRONOPULOS: OPTIMUM DESIGN OF A CODED MASKX-RAY TELESCOPE FOR ROCKET APPLICATIONS. MON. NOT. R. ASTRON. SOC.,177:485-497, 1976 (hereinafter “Gunson”) it is further known to give theopaque elements of the aperture a finite thickness such that theaperture itself acts as a collimator and limits the FOV to the fullycoded FOV. Such a “self-collimating aperture” allows the omission of aseparate collimator in front of the detector.

It should be noted that besides limiting the FOV, a collimator has theundesired property of only transmitting light without attenuation whichis exactly parallel to the optical axis. Any off-axis light passingthrough the collimator is attenuated, the attenuation increasing towardsthe limits of the FOV. At the limits of the FOV, the attenuation is100%, i.e., no light can pass through the collimator at such angles.This effect will be denoted as “collimator attenuation” within thisdocument. Both in the x-direction and in the y-direction, collimatorattenuation is proportional to the tangent of the angle between thelight and the optical axis.

After reconstructing an image from a sensor signal in a coded apertureimaging system, the effect of collimator attenuation may have to bereversed in order to obtain a photometrically correct image. Thisinvolves multiplying each individual pixel value with the inverse of thefactor by which light coming from the direction which the pixel pertainsto, has been attenuated. It should be noted that close to the limits ofthe FOV, the attenuation, especially the collimator attenuation, is veryhigh, i.e. this factor approaches zero. Inverting the collimatorattenuation in this case involves amplifying the pixel values with avery large factor, approaching infinity at the limits of the FOV. Sinceany noise in the reconstruction will also be amplified by this factor,pixels close to the limits of the FOV may be very noisy or evenunusable.

In a coded aperture system according to Fenimore or Gunson, the basicaperture pattern can be characterized by means of an “aperture array” ofzeros and ones wherein a one stands for a transparent and a zero standsfor an opaque aperture element. Further, the scene within the FOV can becharacterized as a two-dimensional array wherein each array elementcontains the light intensity emitted from a single pixel within the FOV.When the scene is at infinite distance from the aperture, it is knownthat the sensor signal can be characterized as the two-dimensional,periodic cross-correlation function between the FOV array and theaperture array. It should be noted that the sensor signal as such has noresemblance with the scene being imaged. However, a “reconstructionfilter” can be designed by computing the two-dimensional periodicinverse filter pertaining to the aperture array. The two-dimensionalperiodic inverse filter is a two-dimensional array which is constructedin such a way that all sidelobes of the two-dimensional, periodiccross-correlation function of the aperture array and the inverse filterare zero. By computing the two-dimensional, periodic cross-correlationfunction of the sensor signal and the reconstruction filter, an image ofthe original scene can be reconstructed from the sensor signal.

It is known from Fenimore to use a so-called “Uniformly RedundantArrays” (URAs) as aperture arrays. URAs have a two-dimensional, periodiccross-correlation function whose sidelobe values are all identical. URAshave an inverse filter which has the same structure as the URA itself,except for a constant offset and constant scaling factor. Suchreconstruction filters are optimal in the sense that any noise in thesensor signal will be subject to the lowest possible amplificationduring the reconstruction filtering. However, URAs can be algebraicallyconstructed only for very few sizes.

It is further known from S. R. GOTTESMAN AND E. E. FENIMORE: NEW FAMILYOF BINARY ARRAYS FOR CODED APERTURE IMAGING. APPL. OPT., 28:4344-4352,1989 (hereinafter “Gottesman”) to use a modified class of aperturearrays called “Modified Uniformly Redundant Arrays” (MURAs) which existfor all sizes p×p where p is an odd prime number. Hence, MURAs exist formany more sizes than URAs. Their correlation properties and noiseamplification properties are near-optimal and almost as good as theproperties of URAs. MURAs have the additional advantage that, with theexception of a single row and a single column, they can be representedas the product of two one-dimensional sequences, one being a functiononly of the column index and the other being a function only of the rowindex to the array. Likewise, with the exception of a single row and asingle column, their inverse filter can also be represented as theproduct of two one-dimensional sequences. This property permits toreplace the two-dimensional in-verse filtering by a sequence of twoone-dimensional filtering operations, making the reconstruction processmuch more efficient to compute.

It is further known from A. BUSBOOM: ARRAYS UNDREKONSTRUKTIONSALGORITHMEN FUER BILDGEBENDE SYSTEME MIT CODIERTERAPERTUR. VDI VERLAG, DUESSELDORF, 1999, ISBN 3-18-357210-9 (hereinafter“Busboom”) to use so-called “Perfect Binary Arrays” (PBAs) which existfor all sizes 3^(s) 2^(r)×3^(s) 2^(r) and all sizes 3^(s) 2^(r−1)×3^(s)2^(r+1) where s=0, 1, 2 . . . and r=1, 2, 3 . . . . Hence, PBAs alsoexist for many sizes, especially for many square sizes with an evennumber of columns and rows. Their correlation properties and noiseamplification properties are as good as those of URAs.

If the scene is at a finite distance from the aperture, a geometricmagnification of the sensor image occurs. It should be noted that apoint source in the scene would cast a shadow of the aperture patternonto the sensor which is magnified by a factor of f=(o+a)/o compared tothe actual aperture size where o is the distance between the scene andthe aperture and a is the distance between the aperture and the sensor.Therefore, if the scene is at a finite distance, the sensor image needsto be filtered with an accordingly magnified version of thereconstruction filter.

If the scene is very close to the aperture, so-called near-field effectsoccur. The “near field” is defined as those ranges which are less than10 times the sensor size, aperture size or distance between aperture andsensor, whichever of these quantities is the largest. If an object is inthe near field, the sensor image can no longer be described as thetwo-dimensional cross-correlation between the scene and the aperturearray. This causes artifacts when attempting to reconstructing the sceneusing inverse filtering. In Lanza, et al., U.S. Pat. No. 6,737,652,methods for reducing such near-field artifacts are disclosed. Thesemethods involve imaging the scene using two separate coded apertureswhere the second aperture array is the inverse of the first aperturearray (i.e. transparent elements are replaced by opaque elements andvice versa). The reconstruction is then computed from two sensor signalsacquired with the two different apertures in such a manner thatnear-field artifacts are reduced in the process of combining the twosensor images.

Coded aperture imaging to date has been limited to industrial, medical,and scientific applications, primarily with x-ray or gamma-rayradiation, and systems that have been developed to date are eachdesigned to work within a specific, constrained environment. For one,existing coded aperture imaging systems are each designed with aspecific view depth (e.g. effectively at infinity for astronomy, or aspecific distance range for nuclear or x-ray imaging). Secondly, todate, coded aperture imaging has been used with either controlledradiation sources (e.g. in nuclear, x-ray, or industrial imaging), orastronomical radiation sources that are relatively stable andeffectively at infinity. As a result, existing coded aperture systemshave had the benefit of operating within constrained environments, quiteunlike, for example, a typical photographic camera using a lens. Atypical photographic camera using a single lens (i.e. a single lens persensor or film frame; stereoscopic cameras have 2 lenses, but utilize aseparate sensor or film frame per lens) is designed to simultaneouslyhandle imaging of scenes containing 3-dimensional objects with varyingdistances from close distances to effective infinite distance; and isdesigned to image objects reflecting, diffusing, absorbing, refracting,or retro-reflecting multiple ambient radiation sources of unknownorigin, angle, and vastly varying intensities. No coded aperture systemhas ever been designed that can handle these types of unconstrainedimaging environments that billions of photographic cameras with singlelenses handle everyday.

Photographic imaging in the optical spectrum using a single lens has anumber of disadvantages and limitations. The main limitation of singlelens photography is its finite depth-of-field (DOF), particularly atlarge aperture settings. Only scenes at a limited DOF can be in focus ina single lens image while any objects closer or farther away from thecamera than the DOF will appear blurred in the image.

Further, a single lens camera must be manually or automatically focusedbefore an image can be taken. This is a disadvantage when imagingobjects which are moving fast or unexpectedly such as in sportsphotography or photography of children or animals, particularly at largeapertures with a short DOF. In such situations, the images may be out offocus because there was not enough time to focus or because the objectmoved unexpectedly when acquiring the image. Single lens photographydoes not allow a photographer to retrospectively change the focus oncean image has been acquired.

Still further, focusing a single lens camera involves adjusting thedistance between one or more lenses and the sensor. This makes itnecessary for a single lens camera to contain mechanically moving partswhich makes it prone to mechanical failure. Various alternatives toglass lenses, such as liquid lenses (see, e.g., B. HENDRIKS & STEINKUIPER: THROUGH A LENS SHARPLY. IEEE SPECTRUM, DECEMBER, 2004), havebeen proposed in an effort to mitigate the mechanical limitations of aglass lens, but despite the added design complexity and potentiallimitations (e.g., operating temperature range and aperture size) ofsuch alternatives, they still suffer from the limitation of a limitedfocus range.

Still further, single lens cameras have a limited dynamic range as aresult of their sensors (film or semiconductor sensors) having a limiteddynamic range. This is a severe limitation when imaging scenes whichcontain both very bright areas and very dark areas. Typically, eitherthe bright areas will appear overexposed while the dark areas havesufficient contrast, or the dark areas will appear underexposed whilethe bright areas have sufficient contrast. To address this issue,specialized semiconductor image sensors (e.g. the D1000 by Pixim, Inc.of Mountain View, Calif.) have been developed that allow each pixel ofan image sensor to sampled each with a unique gain so as to accommodatedifferent brightness regions in the image. But such image sensors aremuch more expensive than conventional CCD or CMOS image sensors, and assuch are not cost-competitive for many applications, includingmass-market general photography.

Because of the requirement to focus, single lenses can provide a roughestimate of the distance between the lens and a subject object. Butsince most photographic applications require lenses designed to have aslong a range of concurrent focus as possible, using focus for a distanceestimate is extremely imprecise. Since a single lens can only be focusedto a single distance range at a time, at best, a lens will provide anestimate of the distance to a single object range at a given time.

Coded Aperture Imaging (CAI) (as disclosed in co-pending applicationentitled “Apparatus And Method For Capturing Still Images And VideoUsing Coded Aperture Techniques,” Ser. No. 11/039,029, filed Jan. 18,2005; hereinafter “CAI Application”) addresses many of the limitationsof a single lens camera. Relative to a single lens camera, CAI makes itpossible to make a thinner camera, a lighter camera, a camera withgreater dynamic range, and also a camera which can reconstruct an imagewhich is in focus throughout a large range of depth in the scene.

A visible light coded aperture camera according to one embodimentdescribed in the CAI Application is illustrated in FIG. 1. Theillustrated embodiment includes a coded aperture 101 placed in front ofa light sensitive grayscale or color semiconductor sensor 104. The codedaperture 1012 is a pattern of circular, square, hexagonal, rectangularor other tiled elements, some of which are transparent to visible light(e.g. element 102) and some of which are opaque (e.g. element 103). Notethat for illustration clarity purposes, coded aperture 101 has very fewtransparent elements. A typical coded aperture may have significantlymore transparent elements (e.g., 50%). Visible light a from2-dimensional or 3-dimensional scene 100 (which may be illuminated byambient or artificial lighting) is projected through the coded aperture101 onto image sensor 104. The camera is capable of limiting the FOV tothe fully coded FOV projected onto the sensor. In one embodiment, thisis implemented by the use of a self-collimating coded aperture 101(utilizing baffles for collimation, as explained below). The spacebetween the coded aperture and the sensor is shielded by a light-opaquehousing 105 (only the outline of which is shown in FIG. 1), preventingany light from reaching the sensor other than by passing through an openelement of the coded aperture.

The camera further includes an image sensor readout subsystem 110 withan interface 109 to the image sensor 104 (which may be similar to thoseused in prior coded aperture systems). The readout subsystem clocks outthe analog image signal from the image sensor 104 and applies analogbuffering, amplification and/or filtering as required by the particularimage sensor. An example of such a readout subsystem 110 that alsoincorporates A/D 120 is the NDX-1260 CleanCapture Image Processor byNuCore Technology, Inc. of Sunnyvale, Calif. The ability to adjust thezero offset 112 and gain 111 to analog pixel values read by the readoutsubsystem 110 (e.g., using at least one operational amplifier (op amp))will increase the dynamic range of the captured image, but is notessential if the image sensor has a sufficient dynamic range for thedesired image quality without a zero-offset and gain adjustment.

In one embodiment, the output of the readout subsystem 110 is coupled byinterface 113 to at least one analog-to-digital converter (A/D) 120which digitizes the analog output. The output of the A/D is coupled viainterface 121 to an image reconstruction processor 130, which in oneembodiment incorporates a Digital Signal Processor (DSP) 132 and RandomAccess Memory (RAM) 131. The digitized image from the interface 121 isstored in RAM 131, and the DSP 132 post-processes the image so as toreconstruct the original scene 101 into a grayscale or color image. Inaccordance with another embodiment, the image reconstruction processor130 incorporates a general purpose CPU such as an Intel CorporationPentium 4®, or similar general purpose processor. In yet anotherembodiment, the image reconstruction processor 130 incorporates anApplication-Specific Integrated Circuit (“ASIC”) which implements partor all of the reconstruction processing in dedicated digital structures.This grayscale or color image reconstructed by reconstruction processor130 is output through interface 133 to be displayed on a display device140.

However, one limitation of CAI is the resolution of the reconstructedimage. The resolution of a CAI camera is limited by the larger of twoprimary factors: (a) the order of the aperture array, and (b) distortionin the projected image caused by diffraction. This is explained furtherin the following paragraphs.

FIG. 2 shows several representative coded aperture array patterns ofMURAs of “order” 101, 61 and 31 (described in more detail in the CAIapplication). FIG. 2 also shows coded aperture array patterns of PBAs oforder 8 and 24. (The PBAs 8 and 24 are shown enlarged relative to theMURAs to better show their patterns.), Note that the coded aperturearray patterns are formed from a square array (with horizontal andvertical dimensions of the specified order) that is repeated twice inthe horizontal and twice in the vertical dimension. So, for example, theMURA 101 pattern has a total size of 202×202. Note also that each of theaperture elements in the arrays is of the same size. Although it appearsthat some of the apertures are larger than others, this is simplybecause adjacent apertures combine to create what appears to be a largeraperture. A CAI camera can not resolve an image that is higherresolution than the order of its coded aperture array. For example, aMURA 101 CAI camera can not resolve an image of higher resolution than101×101 pixels.

For purposes of illustration, FIG. 3 shows one embodiment of the visiblelight coded aperture camera shown in FIG. 1. The embodiment shown inFIG. 3 is not useful for many applications because the resolution of thereconstructed image is only 3×3 pixels, but it is illustrative of how acamera such as that shown in FIG. 1 works. A MURA order 3 (“MURA 3”)aperture array 301 contains 16 open apertures, such as open aperture302, and 20 closed apertures, such as closed aperture 303. Color orgrayscale sensor 304 is the same size as one quadrant (i.e. one 3×3block of apertures) of the MURA 3 aperture array 301 and in thisembodiment it is positioned centered relative to the MURA 3 aperturearray 301.

Orthographic View 320 of FIG. 3 reveals more of the structure of thecamera. Baffles (referred to as “collimators” in the CAI Application)315 serve to collimate the light passing through open apertures, such asopen aperture 302. This restricts the FOV of each aperture projectiononto color or grayscale sensor 304. Closed apertures such as closedaperture 303 are covered with an opaque cover so they do not allow lightto pass through. Sensor 304 is separated from MURA 3 aperture array 301and baffles 317 to allow space for the overlapping projections from eachof the open apertures. The entire unit is contained within a light-tightcamera body 316, which is shown to be transparent for the purposes ofillustration. Note that in this particular example, even if sensor 304is a very high-resolution sensor, only a 3×3 pixel image can bereconstructed.

FIG. 4 illustrates how light is projected through the MURA 3 aperturearray. Illustration 400 shows the MURA 3 aperture array 401 delineatedby a solid black outline, with exemplary open aperture 402 and closedaperture 403. The position of color or grayscale sensor 404 isdelineated by a dotted outline. Open aperture 405 is delineated by adashed line. The light that passes through aperture 405 projects onto asquare area on the sensor plane shown as a gray square 406. Note thatbecause aperture array 401 is shown overlaying the projection inillustration 400, much of projection 406 is obstructed by closedapertures. Nonetheless, the perimeter of projection 406 can be seendelineated by a solid gray outline.

In this embodiment, projection 406 is a square approximately 9 timeslarger than aperture 405 and centered on aperture 405. Depending on howclose or far sensor 404 is to the aperture array, this projection maycorrespond to a wider or narrower FOV. Baffles around aperture 405 (notshown in this illustration, but visible as baffles 317 in FIG. 3) areused in this embodiment to limit the extent of projection 406 toapproximately 9 times larger than the size of aperture 405.

Note that in this embodiment only a small percentage of the area ofprojection 406 overlaps sensor 404. Part of this overlap is visiblethrough an open aperture 409 and part of it is obscured by closedaperture 408.

Illustration 410 shows the overlaying of the 4 projections from theupper right quadrant of aperture array 401. (For clarity, inillustrations 410 and 420, only the outline of MURA 3 aperture array 401is shown.) The 4 open apertures 415 in the upper right quadrant aredelineated with dashed outlines. The 4 projections 416 from these 4apertures are shown as overlapping gray areas. Each projection, like theprojection 406 shown in illustration 400, is a square approximately 9times the size of its aperture and is centered on its aperture, and isdelineated by a solid gray line. To indicate the number of overlappingprojections in each area of the sensor plane, varying levels of grayscale are used to fill each area. The lightest gray indicates 1projection, the next darker indicates 2 projections overlapping, thenext darker indicates 3 projections overlapping, and finally the darkestindicates 4 projections overlapping.

Illustration 420 shows the overlaying of all 16 projections from theentire aperture array 401. The 16 open apertures 425 are delineated bydashed outlines. Each projection, like the projection 406 shown inillustration 400, is a square approximately 9 times the size of itsaperture and centered on its aperture, and is delineated by a solid grayline. To indicate the number of overlapping projections in each area ofthe sensor plane, varying levels of gray scale are used as described inthe previous paragraph. Note that in this embodiment each area of sensor404 is shown covered by 4 overlapping projections. In practice, it iscorrect that there will be 4 overlapping projections over the vastmajority of the sensor area, but because of tolerance variations,diffraction effects, and varying distances to objects in the observedscene, there may be fewer or more overlapping projections near theborders of projections, which are shown as solid gray lines inillustration 411.

Note also that most of the light hitting the MURA 3 aperture array 401is projected beyond the edges of sensor 404, and as a result this lightis not used for the reconstruction. If the area of the rightmost columnof the MURA 3 aperture array 401 is disregarded (since all apertures inthat column are closed, it does not contribute any light to the cameraand can be removed from the system without impacting the imagereconstruction), approximately 13% of the light hitting the remainingarea of the MURA 3 aperture array 401 is actually projected onto thesensor 404. A conventional single f/2.8 lens transmits approximately12.7% of the light hitting the lens, so the 13% light transmissionperformance of this MURA 3 coded aperture array camera can be seen ascomparable to a conventional f/2.8 lens.

Generally speaking, f/2.8 is good light transmission performance for aphotographic lens, so the description of the MURA 3 coded aperturecamera in the last few paragraphs characterizes a camera withpotentially desirable light transmission characteristics. Unfortunately,only a 3×3 pixel image can be reconstructed by the system described.

Each element in a CAI camera acts geometrically like a pinhole in apinhole camera. Light passing through each aperture makes a projectiononto the sensor, just as it would in a pinhole camera. And like apinhole camera, a CAI camera is subject to the diffraction effects oflight passing through a pinhole. In a pinhole, these diffraction effectscreate a point source projected pattern commonly known as the “Airydisk”. The primary lobe of the Airy disk roughly defines the smallestresolvable spot size from a given pinhole camera projection. At a givendistance from the pinhole to the sensor, the Airy disk increases in sizeas the pinhole decreases in size. From a geometric point of view, theresolution (i.e. minimum point source projection spot size) of imagesfrom a pinhole camera also increases as the pinhole gets smaller. So,for any given distance of pinhole to sensor, there is an optimum pinholesize where the point source projection spot size equals the size of theprimary lobe of the Airy disk. If the pinhole is made smaller than thisoptimum size, resolution decreases because the Airy disk increases insize. If the pinhole is made larger than this optimum size, resolutiondecreases because a point source projection spot size increases. Sincethe characterization of resolution of a pinhole camera is subjective,different formulae have been proposed for calculating the optimalpinhole diameter. One such formula is A=SQRT(55F), where A is thepinhole diameter in thousandths of an inch, F is the camera focal lengthin inches, and SART( ) is the square root function.

Note that achievable resolution in a pinhole camera increases as thefocal length of the camera increases. Unfortunately, the physical sizeof the camera typically increases in proportion to the focal length, andas a result, a very large camera is needed for high resolution pinholeimages. For example (using the formula A=SQRT(55F)), the optimal pinholesize of a 1″ focal length (i.e. 1″ thick) pinhole camera is about0.007″. For a “normal” viewing angle of about 53°, this results in abouta 134.8 pixel diagonal dimension, or about a 95×95 pixel resolutionimage. The optimal pinhole size of a 10″ focal length (i.e. 10″ thick)pinhole camera is about 0.023″. With a 53° viewing angle, this resultsin about a 426.4 diagonal resolution, or about a 301×301 resolutionimage. (Note that different photographers will use different subjectivecriteria in assessing the resolvable resolution of a pinhole camera. Theresolution calculated here is based on one interpretation of resolvableresolution. Other interpretations may lead higher or lower resolutionassessments, but will normally be within a 2× range higher or lower thanthe numbers presented here.)

Like pinhole cameras, visible light CAI cameras are also subject todiffraction effects which may result in resolution/size trade-offs. Thediffraction patterns are more complex than pinhole diffraction patternsbecause of the complexity of the aperture patterns, and consequently,determining the impact on image resolution and/or camera sizerequirements is more complex. But because the pixel resolution of theCAI image can be no higher than the order of the aperture array, toachieve a high-resolution image it is necessary to utilize high orderaperture arrays which can potentially exhibit worse diffraction effectsthan lower order aperture arrays or, alternatively, require longer focallengths (and, as a result, larger camera sizes) to mitigate thosediffraction effects.

Another approach to improving the performance of a lens system in adigital camera is a plenoptic camera. The basic concept of a plenopticcamera is described in U.S. Pat. No. 5,076,687. Although the word“plenoptic” is not used in the patent, the device referenced in thepatent is called a “plenoptic camera” by its inventor in a web pagedescribing the camera at:http://www-bcs.mit.edu/people/jyawang/demos/plenoptic/plenoptic.html. In2005, Stanford University researchers published a paper (Stanford TechReport CTSR 2005-02) describing an application of a plenoptic cameraimplementation that achieves the DOF of a conventional f/22 lens whilecapturing the equivalent light from the scene that would be gathered byan f/4 lens. Unfortunately, this increase in light gathering abilitycomes at a theoretically linear cost of image resolution. The prototypeconstructed by the team resulted in about 2× beyond the theoreticalresolution losses, so with a 4000×4000 pixel sensor they were able toreconstruct only a 296×296 image which exhibited the f/22 DOF with f/4light capture (i.e. a 16 megapixel sensor yielded a 90 kilopixel image).While such a system might be useful for certain specializedapplications, the enormous losses of sensor resolution would likely makesuch a system non-competitive for general photographic applications.

SUMMARY

An apparatus and method are described for capturing images. In oneembodiment, the apparatus comprises: a coded lens array including aplurality of lenses arranged in a coded pattern with opaque materialblocking array elements not containing lenses; and a light-sensitivesemiconductor sensor coupled to the coded lens array and positioned at aspecified distance behind the coded lens array, the light-sensitivesensor configured to sense light transmitted through the lenses in thecoded lens array.

BRIEF DESCRIPTION OF THE DRAWINGS

A better understanding of the present invention can be obtained from thefollowing detailed description in conjunction with the drawings, inwhich:

FIG. 1 illustrates a visible light coded aperture camera according toone embodiment of the invention.

FIG. 2 illustrates three exemplary MURA patterns and two exemplary PBApatterns employed in accordance with the underlying principles of theinvention.

FIG. 3 illustrates the configuration of a MURA order 3 coded aperturearray, baffles, sensor, and a camera body in accordance with oneembodiment of the invention.

FIG. 4 illustrates the projection of light from transparent apertures ina MURA 3 coded aperture array in accordance with one embodiment of theinvention.

FIG. 5 illustrates a coded lens camera according to one embodiment ofthe invention.

FIG. 6 illustrates the configuration of a MURA order 3 coded lens array,baffles, sensor, and a camera body in accordance with one embodiment ofthe invention.

FIG. 7 illustrates the projection of light from transparent apertures ina MURA 3 coded lens array in accordance with one embodiment of theinvention.

FIG. 8 illustrates a side view of a MURA order 3 coded lens camera inaccordance with one embodiment of the invention.

FIG. 9 illustrates an exemplary RGB Bayer Pattern employed in oneembodiment with the invention.

FIG. 10 illustrates image sensors implemented as a multi-layer structureand used in one embodiment of the invention.

FIG. 11 a illustrates one embodiment of the invention in which an outputsignal is digitized by an analog-to-digital converter (A/D) in order toallow digital image reconstruction and post-processing.

FIG. 11 b illustrates a process for selecting zero offset and gain inaccordance with one embodiment of the invention.

FIG. 12 illustrates a coded lens imaging characteristic and a typicallens imaging characteristic.

FIG. 13 illustrates a graph showing typical CMOS and CCD image sensortransfer characteristics.

FIG. 14 illustrates a side view of a MURA order 3 coded lens camera withmulti-element lens in accordance with one embodiment of the invention.

FIG. 15 illustrates a gearing arrangement for simultaneously focusingall of the lenses in a coded lens array in accordance with oneembodiment of the invention.

FIG. 16 illustrates a side view of a multi-element coded lens systemwith a gearing system for simultaneously focusing all the lenses in acoded lens array in accordance with one embodiment of the invention.

FIG. 17 a illustrates three examples of a projection and reconstructionof three flat scenes at a known range using a MURA 3 coded lens array inaccordance with one embodiment of the invention.

FIG. 17 b illustrates three examples of a projection and reconstructionof three flat scenes at a known range using a PBA 24 coded lens array inaccordance with one embodiment of the invention.

FIG. 18 illustrates a reconstruction of an image at different ranges toidentify the correct range in accordance with one embodiment of theinvention.

FIG. 19 illustrates an image in which a person is standing close to acamera, while mountains are far behind the person.

FIG. 20 illustrates how the person from FIG. 19 can readily be placed ina scene with a different background.

FIG. 21 illustrates a photograph of an exemplary motion capture session.

DETAILED DESCRIPTION

A system and method for capturing still images and video using codedlens imaging techniques is described below. In the description, for thepurposes of explanation, numerous specific details are set forth inorder to provide a thorough understanding of the present invention. Itwill be apparent, however, to one skilled in the art that the presentinvention may be practiced without some of these specific details. Inother instances, well-known structures and devices are shown in blockdiagram form to avoid obscuring the underlying principles of theinvention.

Camera System Architecture

A visible light coded lens array camera. for either single shot imagesor sequential (e.g. video) images, including readout electronics anddisplay, according to one embodiment of the invention, is illustrated inFIG. 5. The illustrated embodiment includes a coded lens array 501placed in front of a light sensitive grayscale or color semiconductorsensor 504. The coded lens array 501 is a pattern of circular, square,hexagonal or rectangular (or any pattern that can be tiled on a plane)apertures, some of which are transparent (i.e. “open”) to visible light(e.g. element 502) and some of which are opaque (i.e. “closed) tovisible light (e.g. element 503). Each open aperture, such as 502, iscovered by (or contains) a lens such as 508, so that virtually all ofthe light passing through the open aperture passes through the lens. Atypical coded lens array has approximately 50% transparent apertures,each with a lens. The coded lens array pattern shown is a MURA order 3with a 4/5 ratio of transparent to opaque apertures. Visible light afrom 2-dimensional or 3-dimensional scene 500 (which may be illuminatedby ambient or artificial lighting) is projected through the lenses andopen apertures of coded aperture array 501 onto image sensor 504. (Thecamera is capable of limiting the FOV to the fully coded FOV projectedonto the sensor. The light contributions of overlapping projections inthis fully coded FOV is shown in illustration 620 of FIG. 6.) In oneembodiment, this is implemented by the use of a self-collimating codedlens array 501 (self-collimation is accomplished through baffles 517behind the coded lens array 501, which are explained below). The spacebetween the coded lens array and the sensor is shielded by alight-opaque housing 516 (only the outline of which is shown in FIG. 5),preventing any light from reaching the sensor other than by passingthrough a lens and open aperture of the coded lens array 501.

The camera further includes an image sensor readout subsystem 510 withan interface 509 to the image sensor 504. The readout subsystem clocksout the analog image signal from the image sensor 504 and applies analogbuffering, amplification and/or filtering as required by the particularimage sensor. An example of such a readout subsystem 510 that alsoincorporates A/D 520 is the NDX-1260 CleanCapture Image Processor byNuCore Technology, Inc. of Sunnyvale, Calif. The ability to adjust thezero offset 512 and gain 511 to analog pixel values read by the readoutsubsystem 510 (e.g., using at least one operational amplifier (op amp))will increase the dynamic range of the captured image, but is notessential if the image sensor has a sufficient dynamic range for thedesired image quality without a zero-offset and gain adjustment.

In one embodiment, the output of the readout subsystem 510 is coupled byinterface 513 to at least one analog-to-digital converter (A/D) 520which digitizes the analog output. The output of the A/D is coupled viainterface 521 to an image reconstruction processor 530, which in oneembodiment incorporates a Digital Signal Processor (DSP) 532 and RandomAccess Memory (RAM) 531. The digitized image from the interface 521 isstored in RAM 531, and the DSP 532 post-processes the image so as toreconstruct the original scene 500 into a grayscale or color image. Inaccordance with another embodiment, the image reconstruction processor530 incorporates a general purpose CPU such as an Intel CorporationPentium 4®, or similar general purpose processor. In yet anotherembodiment, the image reconstruction processor 530 incorporates anApplication-Specific Integrated Circuit (“ASIC”) which implements partor all of the reconstruction processing in dedicated digital structures.This grayscale or color image reconstructed by reconstruction processor530 is output through interface 533 to be displayed on a display device540.

FIG. 6 shows one embodiment of the visible light coded lens array camerashown in FIG. 5. A MURA order 3 (“MURA 3”) lens array 601 contains 16open apertures, such as open aperture 602, and 20 closed apertures, suchas closed aperture 603. Each open aperture, such as 602, contains onelens. In the illustrated embodiment, the lenses are round, but inalternative embodiments the lens may be other shapes (e.g. squares orhexagons) that may more completely fill the open aperture 602 area. But,regardless of the shape of lens 608 in the present embodiment, anyremaining area of the open aperture 602 not filled by lens 608 must beopaque or nearly opaque. Color or grayscale sensor 604 is the same sizeas one quadrant (i.e. one 3×3 block of apertures) of the MURA 3 aperturearray 601 and in this embodiment it is positioned centered relative tothe MURA 3 aperture array 601, as shown in illustration 610.(Illustration 610 shows sensor 604's placement location behind MURA 3lens array 601 by showing it through the circles that illustrate theshape of the lenses. This is done simply for the sake of illustration,and this may not what would be seen upon visual inspection of an actualsystem due to the refraction effects of the lenses if an observer wouldlook through them.)

Orthographic View 620 of FIG. 6 reveals more of the structure of thecamera. Baffles (referred to as “collimators” in the CAI Application)617 serve to collimate the light passing through the lens and openapertures, such as open aperture 602 and lens 608. This restricts theFOV of each aperture projection onto color or grayscale sensor 604.Closed apertures such as closed aperture 603 are covered with an opaquecover so they do not allow light to pass through. Sensor 604 isseparated from MURA 3 aperture array 611 and baffles 617 to allow spacefor the overlapping projections from each of the open apertures. Theentire unit is contained within a light-tight camera body 616, which isshown to be transparent for the purposes of illustration.

FIG. 7 illustrates how light is projected through the MURA 3 coded lensarray 701. Illustration 700 shows the MURA 3 coded lens array 701, withexemplary open aperture and lens 702 and closed aperture 703. Theposition of color or grayscale sensor 704 that would be located behindcoded lens array 701 is delineated by a dotted outline. Lens 705 isdelineated by a dashed line. The light that passes through lens 705projects onto a square area on the sensor plane shown as a gray square706. Note that because aperture array 701 is shown in illustration 700as overlaying the projection, much of projection 706 is obstructed byclosed apertures. Nonetheless, the perimeter of projection 706 can beseen delineated by a solid gray outline.

In this embodiment, projection 706 is a square approximately 9 timeslarger than open aperture square around lens 705 and centered on lens705. Depending on how close or far sensor 704 is to the aperture array,this projection may correspond to a wider or narrower FOV. Bafflesaround open aperture 705 (not shown in this illustration, but visible asbaffles 617 in FIG. 6 are used in this embodiment to limit the extent ofprojection 706 to approximately 9 times larger than the size of lens705.

Note that in this embodiment only a small percentage of the area ofprojection 706 overlaps sensor 704. Part of this overlap is visible(illustratively, although not necessarily physically) through the lensof open aperture 709 and part of it is obscured (illustratively) byclosed aperture 708 and the area around the lens in open aperture 709.

Illustration 710 shows the overlaying of the 4 projections from theupper right quadrant of aperture array 701. (For clarity in illustration710 and 720, only the outline of MURA 3 coded lens array 701 is shown.)The 4 lenses of open apertures 715 in the upper right quadrant aredelineated with dashed outlines. The 4 projections 716 from these 4lenses are shown as overlapping gray areas. Each projection, like theprojection 706 shown in illustration 700, is a square approximately 9times the size of the open aperture square surrounding its lens and iscentered on its lens, and is delineated by a solid gray line. Toindicate the number of overlapping projections in each area of thesensor plane, each area is filled with varying levels of gray scale. Thelightest gray indicates 1 projection, the next darker indicates 2projections overlapping, the next darker indicates 3 projectionsoverlapping, and finally the darkest indicates 4 projectionsoverlapping.

Illustration 720 shows the overlaying of all 16 projections from theentire aperture array 701. The 16 lenses of all open apertures 725 aredelineated by dashed outlines. Each projection, like the projection 706shown in illustration 700, is a square approximately 9 times the size ofthe open aperture square surrounding its lens and centered on its lens,and is delineated by a solid gray line. To indicate the number ofoverlapping projections in each area of the sensor plane, varying levelsof gray scale are used as described in the previous paragraph. Note thatin this embodiment each area of sensor 704 is shown covered by 4overlapping projections. In practice, it is correct that there will be 4overlapping projections over the vast majority of the sensor area, butbecause of tolerance variations, diffraction effects, lens aberrationsand varying distances to objects in the observed scene, there may befewer or more overlapping projections near the borders of projections,which are shown as solid gray lines in illustration 720.

Note also that most of the light hitting the MURA 3 coded lens array 701is projected beyond the edges of sensor 704, and as a result this lightis not used for the reconstruction. If the area of the rightmost columnof the MURA 3 coded lens array 701 is disregarded (since all aperturesin that column are closed, it does not contribute any light to thecamera and can be removed from the system without impacting the imagereconstruction), approximately 10.2% (because round lenses are used inthis embodiment, if square lenses were used in an alternate embodiment,the number would be approximately 13%) of the light hitting theremaining area of the MURA 3 aperture array 701 is actually projectedonto the sensor 704. A conventional single f/3.1 lens transmitsapproximately 10.2% of the light hitting the lens, so the 10.2% lighttransmission performance of this MURA 3 coded aperture array camera canbe seen as comparable to a conventional f/3.1 lens.

Generally speaking, f/3.1 is good light transmission performance for aphotographic lens, so the description of the MURA 3 coded lens arraycamera in the last few paragraphs characterizes a camera withpotentially desirable characteristics. And unlike a MURA 3 codedaperture array camera, such as that illustrated in FIGS. 3 and 4, whichis limited to a 3×3 pixel resolution in the reconstruction, the MURA 3coded lens array camera illustrated in FIGS. 5, 6 and 7 is capable ofreconstructing an image at least up to the approximate diffractionlimits of each of the lenses in the MURA 3 coded lens array. Forexample, in the case of lenses 12 mm lenses with a 36 mm focal lengthand a 53 degree FOV, more 2000×2000 resolution (4 megapixels) isachievable within the diffraction limits.

The preceding illustrated examples show the size of the sensor as beingapproximately equal to the size of one quadrant (i.e. one-half size ineach dimension) as the size of the coded lens array. Although this is atypical configuration, in one embodiment the sensor dimensions areindependent from the coded lens array dimensions, but the system isconfigured in such a way that the coded lens array projects a patternonto the sensor that is equivalent to the pattern that would have beenprojected had the sensor been equal to the size of one quadrant of acoded lens array and with appropriate spacing and focal length such asthe coded lens camera configurations described herein. In other words,the reconstruction of the image using the techniques described hereinare reliant on the configuration of overlapping pattern of images of thescene projected onto the sensor, not on the particular configuration ofthe coded lens array relative to the sensor. If a different coded lensarray configuration than one described herein can achieve a similaroverlapping pattern on the sensor, then the image reconstruction will bethe same. For example, if telephoto lenses in a MURA 3 pattern arepositioned far from the sensor, but the optical path of each is angledin such a way that the projected pattern on the sensor is the same asthe pattern shown in FIG. 7, then the image can still be reconstructedcorrectly.

According to one embodiment of the system illustrated in FIG. 5, theresulting output 533 from the reconstruction processor is a2-dimensional array of grayscale or color pixels representing the scenewithin the FOV of the camera. In one embodiment, the pixel data istransmitted through a digital interface to a computer (or other imageprocessing device). Thus, the output of the coded aperture camera willappear to any attached device as if it is the output of a conventionaldigital camera. The digital interface for transferring the reconstructedimage data may be any digital interface capable of handling thebandwidth from the camera for its required application such as forexample, a IEEE1394 (“FireWire”) interface or a USB 2.0 interface (whichwould be suitable for current still and video camera applications). Ofcourse, the underlying principles of the invention are not limited toany particular digital interface. Preferably, the camera includes adisplay 540 (e.g., an LCD or OLED display), for presenting thereconstructed images to the photographer, but in this embodiment,display device 540 and interface 533 are optional.

According to one embodiment, the camera does not include reconstructionprocessor 530. Instead, the digitized image data from the A/D converter520 is coupled through interface 521 to an output buffer where the imagedata is packetized and formatted to be output through a digitalinterface. The digital interface would typically be coupled to anexternal computing means such as a personal computer, either to beprocessed and reconstructed immediately, or stored on a mass storagemedium (e.g., magnetic or optical disc, semiconductor memory, etc.) forprocessing and reconstruction at a later time. Preferably, the externalcomputing device has a display for presenting the reconstructed imagesto the photographer. Alternatively, or in addition, the digitalinterface is coupled directly to a mass storage medium (e.g., magneticor optical disc, semiconductor memory, etc.). The digital interface fortransferring the reconstructed image data could be any digital interfacecapable of handling the bandwidth from the camera for its requiredapplication (e.g., IEEE1394 (“FireWire”) interface or a USB 2.0interface).

Coded Lens Array Pattern Construction

According to one embodiment of the invention, the coded lens array 501is a Modified Uniformly Redundant Array (“MURA”) pattern. According toanother embodiment of the invention, the coded lens array 501 is aPerfect Binary Array (“PBA”) pattern. According to another embodiment ofthe invention, the coded lens array 501 is a Uniformly Redundant Array(“URA”) pattern. And according to yet another embodiment of theinvention, the coded lens array 501 is a random pattern (although theperformance of the system typically will not be as optimal with a randompattern as it will with a MURA, PBA, or URA). Typically, the basicaperture pattern would be the same size as the sensor, and the overallcoded lens array would be a 2×2 mosaic of this basic aperture pattern.Each transparent aperture in the array contains a lens. Three exemplaryMURA patterns and one PBA pattern are illustrated in FIG. 2. MURA 101 isa 101×101 element pattern, MURA 61 is a 61×61 element pattern, and MURA31 is a 31×31 element pattern. PBA 8 is a 8×8 element pattern, and PBA24 is a 24×24 element pattern. The PBA patterns are illustrated asenlarged relative to the MURA patterns. In each pattern, each black areais opaque and each white area is transparent (open) and would contain alens.

Coded Lens Array Fabrication

In one embodiment, the coded aperture consists of a microlens array suchas those manufactured by Suss Micro-optics of Neuchatel, Switzerland. Amicrolens array is an array of typically plano-convex lenses fabricatedin a typically a rectilinear or hexagonal grid. In one embodiment, amicrolens array would be used for the coded lens array with a lens ateach location on the grid, but those lenses occurring at “closed”aperture location would be painted over with an opaque paint or anopaque material would be lithographically coated at the “closed”aperture locations.

In another embodiment a microlens array would be fabricated with onlylenses at locations of an “open” aperture in the coded lens array.“Closed” aperture locations in the coded lens array would be eitherpainted with an opaque paint, or a opaque material would belithographically coated at the “closed” aperture locations.

Baffles, Camera FOV, and Light Attenuation

According to the present invention the distance between the coded lensarray and the sensor plane is chosen in such a way that each of theprojections of the individual lenses is in focus. For imaging an objectat infinity, the sensor plane is therefore placed at the focal plane ofthe lenses. For imaging an object at a finite distance, the sensor planemight be placed slightly behind the focal plane of lenses in order tofocus at the desired distance. Unlike in coded aperture imaging, thedistance between the coded lens array and the sensor plane may thereforenot be chosen arbitrarily, but a constraint between focal length, imageplane to sensor plane distance, and distance of the object to be imagemust be observed.

One embodiment of the camera employs techniques to limit the FOV (FOV)to the fully coded FOV (FCFOV). Alternatively, the techniques oflimiting the FOV may be dimensioned in such a way that the FOV isslightly larger than the FCFOV, i.e., in such a way that the FOV iscomposed of the FCFOV plus a small part of the partially coded FOV(PCFOV). This way, the FOV of a coded lens camera can be increased atthe expense of only a very minor degradation in image quality.

According to one embodiment, FOV limitation is achieved by placingbaffles either in front of or behind the lenses in order to limit themaximum angles at which rays can pass through the coded lens array andreach the sensor.

Note that the length of the baffles determines the size of the FOV: Thelonger the baffles, the narrower the FOV of the coded lens camera.

FIG. 8 illustrates a side view of the projected FOVs of each of thelenses in a MURA 3 coded lens camera. In this example, the baffles 801are placed behind the lenses 802, i.e. on the side of the lens facingthe sensor 804. It should be noted, however, that the baffles may alsobe placed in front of the lenses, i.e. on the side of the lens facingthe scene.

However, placing the baffles behind the lenses has the advantage thatthe exit pupil 803 of the lens system is moved closer towards the sensorplane. This way the size of the diffraction patterns caused by each lensis reduced and hence the achievable resolution of the overall imagingsystem is increased.

FIG. 8 further shows how the FOV of each lens is determined by themarginal rays 805, passing through the edges of the lens and passingjust by the edge of the baffles on the opposite side. Let l denote thelength of the baffles (l=18 mm in FIG. 8) and let further d denote thediameter of a single lens. Then, as can be seen from FIG. 8, the angularfield of view α is given by

tan α/2=d/l

or

α=2 atan(d/l).

In the example shown in FIG. 8 where d=12 mm and l=18 mm, an angularfield of view of α=67.38° results.

The right hand illustration 810 of FIG. 8 shows how the projectionscaused by the individual lenses overlap in the sensor plane. Each lenshas the same angular field of view. However, due to the displacement ofthe lenses towards each other, there is a parallax for objects at afinite distance. Therefore, the field of view of the overall imagingsystem is approximately the same as the field of view of an individuallens, but may be slightly larger for objects at a finite distance due tothis parallax effect.

It should be noted that FIG. 8 shows a complete row of lenses. However,in a coded lens imaging system, some of the positions in each row willnot contain any lens but be blocked. The figure only shows the completerow of lenses for illustrative purposes. Different rows of lenses in acoded lens array will contain lenses in different positions. Sincetypically each position will contain a lens in at least one row, theoverall field of view can be derived as depicted in FIG. 8.

When using baffles, light passing through the coded lens array parallelto the optical axis will not be attenuated. However, light passingthrough the coded lens array at an angle with respect to the opticalaxis will be partially blocked by the baffles.

As a result, after imaging and reconstructing a scene in a coded lenscamera, the sensitivity of the camera is higher in the center of the FOV(light parallel to the optical axis) than it is towards the edges of theFOV (larger angles with respect to the optical axis), due to the baffleattenuation. Thus, when imaging a constant-intensity surface, thereconstruction will be bright in the center and darker and darkertowards the edges of the image. Therefore, in one embodiment of theinvention, baffle attenuation is compensated for by multiplying eachpixel of the reconstructed image with the inverse of the baffleattenuation the pixel has been subjected to. The baffle attenuation isknown from the geometry of the lenses and baffles. This way, in theabsence of any noise, a constant-intensity surface is reconstructed to aconstant-intensity image.

It should be noted, however, that inverting the baffle attenuation alsocauses any noise in the reconstruction to be amplified with the samefactor as the signal. Therefore, the signal-to-noise ratio (SNR) of thereconstructed image is highest in the center of the image and decreasestowards the edges of the image, reaching the value zero at the edges ofthe FOV.

According to one embodiment of the invention, this problem is alleviatedby using only a central region of the reconstructed image whilediscarding the periphery of the reconstructed image. According toanother embodiment, the problem is further alleviated by applying anoise-reducing smoothing filter to image data at the periphery of thereconstructed image.

From the literature, Wiener filters are known to be optimumnoise-reducing smoothing filters, given that the signal-to-noise ratioof the input signal to the Wiener filter is known. In the reconstructedimage of a coded lens camera, the signal-to-noise ratio varies acrossthe image. The SNR is known for each pixel or each region of thereconstructed image. According to one embodiment, noise-reduction isachieved by applying a local Wiener filtering operation with the filtercharacteristic varying for each pixel or each region of thereconstructed image according to the known SNR variations.

Coded Lens Array DOF

Unlike a coded aperture camera, which projects an image in focus at allscene object distances, a coded lens camera is subject to the focuslimitations of the lenses in its coded lens array. Typically, in aconventional single lens camera, the Depth of Field (DOF) (i.e. therange from near focus to far focus) of the camera is inverselyproportional to the camera's light gathering capability. This is becausethe DOF is typically increased by narrowing the aperture of the lens,which reduces the light from the scene that reaches the sensor.

Although a coded lens camera does have focus limitations, a principaladvantage of the coded lens camera over a conventional single lenscamera is that as the effective lens aperture is narrowed to increasethe DOF, the amount of light from the scene reaching the sensor is notsubstantially reduced.

Consider the following: A coded lens array typically has about 50%transparent apertures with lenses and 50% opaque apertures, so typically50% of the light from the scene passes through the coded lens array. Theoverlapping projections of the coded lens array typically projects ontoan area 4 times the area of the sensor, so approximately 25% of theprojected light hits the sensor. So, in total, typically 25%*50%=12.5%of the light from the scene that is incident upon the coded lens arrayreaches the sensor. (Of course, less light may be transmitted due toattenuation from using round lenses instead of square lenses, thebaffles, lens imperfections, and aberrations, and also, more light maybe transmitted because a given aperture pattern may have more open thanclosed apertures, but geometrically, 12.5% represents the average lighttransmission of square apertures with 50% open apertures and is areasonable approximation for a coded lens system.) 12.5% lighttransmission is approximately equivalent to a f/2.8 aperture on a singlelens (which has 12.7% light transmission).

With a typical single lens system an f/2.8 aperture is a very wideaperture setting. On a 50 mm lens, f/2.8 corresponds to a 17.9 mmaperture. Consider a Nikon D100 6 megapixel camera with a 50 mm lens. Ifthe lens is focused on a subject at a 25′ (25 foot) distance, the nearfocus limit is approximately 21.3′ and the far focus limit isapproximately 30.2′ (30.2′−21.3′=8.82′ of total DOF). (Note: focuslimits are subjective and will vary from photographer to photographer,but the same criteria are utilized for the different conditionsconsidered in this section, so the results can be considered relative toone another. These calculations were made using a Depth of Field onlinecalculator at http://www.dofmaster.com/dofjs.html). Any object in thescene closer than the near focus or farther than the far focus will besubject to a reduction in sharpness. Although 8.82′ is a short DOF, thef/2.8 setting passes about 12.7% of the light from the scene.

Consider now an f/16 setting for the same Nikon D100 with a 50 mm lens.Now the aperture diameter is only 3.1 mm and only 0.4% of the light fromthe scene reaches the sensor. If the lens is focused on a subject at a25′ distance, the near focus limit is approximately 13′ and the farfocus limit is 805′. So, everything in the scene from 13′ to 805′ is infocus, for a 792′ DOF. Clearly, this is a dramatic improvement in DOFover the 8.82′ DOF at f/2.8. But it comes at a dramatic cost in lighttransmission. f/16 only transmits 0.4%/12.7%=3% of the light transmittedby f/2.8, so it can only be used with very well-illuminated scenes.

Consider the same Nikon D100, but instead of using a single conventional50 mm lens, a 50 mm square PBA 8 coded lens array is utilized, againfocused on an object 25′ in the distance. The PBA 8 pattern shown inFIG. 2 would be utilized, with a lens placed in each transparent (i.e.illustrated as white) aperture of the PBA 8. Since a PBA 8 is a 16×16aperture array and in this embodiment it is 50 mm in length on eachside, each lens would be about 3.1 mm in diameter, which is about thesame diameter as a conventional single 50 mm lens stopped down to f/16.And as a result, the DOF of the PBA 8 coded lens array would be roughlythe same as the DOF of a conventional 50 mm lens stopped down to f/16.But, because the coded lens array transmits approximately 12.5% of thelight from the scene, its light transmission is similar to f/2.8. So,this embodiment of a coded lens array has a DOF comparable to an f/16conventional lens with the light transmission characteristics of anf/2.8 conventional lens.

In another embodiment, the same coded lens array described in theprevious paragraph is used with a Nikon D100 camera, but the coded lensarray is focused on an object 26′ in the distance instead of 25′ away.In this case the near focus limit is 12.9′ and the far focus limit isinfinity. Since everything is in focus from a certain distance throughinfinity, the coded lens array is functioning as a “hyperfocal lens”,with its focus distance set to the “hyperfocal distance”. Thisconfiguration is useful for certain applications where all of theobjects in the scene are at least 12.9′ away, and then the lenses in thecoded lens array can be set to a fixed focus and do not need to beadjusted. Note that if an object in the scene is slightly closer than12.9′, it still may be usefully imaged. It simply will not be capturedat the highest resolution, but as objects continue to get closer than12.9′, they will get increasingly fuzzier (i.e. lower resolution). So,for applications that require high resolution for objects closer than12.9′, a focusing means for the lenses in the coded lens array will berequired.

Coded Lens Array Aberration Correction and Focusing

For clarity of illustration, the coded lens arrays shown in most of thefigures have only a single lens element in each transparent aperture.Although this may be sufficient for some applications, in otherapplications, it is desirable to use multiple lens elements to correctfor image aberrations, such as geometric distortion, coma, and chromaticaberrations. For over a century, an entire lens industry has beendevoted to designing multi-element lenses to address lens aberrationissues, and this vast corpus of prior art work will not be repeatedhere. Suffice it to say that typically, 3 elements or more are neededfor photographic-quality imaging, and further, that typically, one ormore of these elements needs to translate back-and-forth on the opticalaxis for focusing, unless the camera has a fixed focus. Frequently, suchback-and-forth motion is accomplished by a rotating mechanism that turnsa collar around part or all of the lens, which in turn engages a threadwhich moves one or more of the lens elements along the optical axis.

FIG. 14 illustrates a side view of a coded lens array with three-elementlenses. The lens shapes shown are simply for illustrative purposes, andthe actual lens shapes would vary depending on the opticalcharacteristics desired, using any of a vast number of prior artphotographic lens designs. Each aperture would have 3 such lenses in astack within one or more concentric cylinders. Baffles would extendbehind the last lens toward the sensor so as to limit the FOV of theprojection. Note that each aperture position is shown containing a stackof lenses in this illustration. In practice, opaque apertures would notcontain lenses, or they would be covered so as not to permit light topass through them.

FIG. 15 illustrates an arrangement of gears with hollow centers within acoded lens array, each gear rotating around either a lens (if thelocation is a transparent aperture) or rotating over an opaque aperturewithout a lens. (For the sake of illustration, the teeth of adjacentgears are not touching each other, but in practice they would typicallyfit together snugly.) Gear 1501 is coupled to the shaft of an electricmotor, which is either manually controlled or is controlled by anauto-focus mechanism. As the electric motor turns, it turns gear 1501,which in turn transfers the rotational motion to all the gears in thecoded lens array. By way of example, if gear 1501 turns clockwise, itturns gear 1502 counterclockwise, which then turns gears 1503 and 1504both clockwise, and then gears 1503 and 1504 both turn gear 1505counter-clockwise. Extending this example, it can be seen that themotion of gear 1501 turns all of the gears in the coded lens array, witheach successive gear in the horizontal or vertical direction turning theopposite way.

FIG. 16 shows a side view of a three-element coded lens array utilizingthe gearing system shown in FIG. 15. For the purposes of illustration,all lens array positions are shown with lenses. In practice, opaque lensarray positions would not have lenses and would have their aperturesclosed so they block light. In this embodiment, each lens array positionhas two fixed lenses 1601 and 1602, and one lens 1603 that translatesback-and-forth along the optical axis.

Electric motor 1620 is powered by either a manual or auto-focus means,and it turns gear 1621, which in turn drives the other gears in thecoded lens array, as previously described in FIG. 15, including FIG.16's gear 1604. Gear 1604 turns hollow cylinder 1605, which in turndrives hollow cylinder 1606, which holds lens 1603. Hollow cylinder 1606is coupled to hollow cylinder 1605 in such a way that it is able totranslate back-and-forth along the optical axis (left-to-right as shownin FIG. 16). Hollow cylinder 1606 has screw thread 1607 on its outsidesurface, which notches pins such as pin 1608 that are secured tostructure 1609. As hollow cylinder 1606 rotates, screw thread 1607causes it to translate back-and-forth along the optical axis.

As can be seen in FIG. 15, each subsequent gear in the coded lens arrayrotates in the opposite direction. As a result each subsequent hollowcylinder holding a lens is threaded with the opposite pitch, such asscrew thread 1610 has opposite pitch of screw thread 1607. In this way,the middle lenses of the lens array all move in the same direction whenthe electric motor 1620 actuates gear 1621, despite the fact each othergear position is rotating in an opposite direction.

In this embodiment, the same structure 1609 that holds the lens arraymechanism continues behind the lenses to form the baffles. Suchstructure 1609 may be made of a metal such as aluminum, plastic, or anyother sufficiently sturdy, but light-opaque material. Note that FIG. 16shows a side view, but in practice the baffle form a box around theperimeter of each transparent aperture, and function to limit the FOV ofthe projection from each lens stack that projects onto sensor 1630.

Sensor Pixel Size and Lens Size

Unlike in coded aperture imaging where sensor pixel size and apertureelement size are typically chosen such as to be in the same order ofmagnitude, in coded lens imaging the individual lenses may be muchlarger than the sensor pixel size.

In one embodiment, the sensor pixel size is chosen such as to be in thesame order of magnitude as the resolution of the coded lens array. Itshould be noted that this resolution is determined by the diffractionpatterns of the individual lenses. If the sensor pixel size is chosensignificantly larger than the size of the diffraction patterns,resolution of the imaging system is wasted. If, on the other hand, thesensor pixel size is chosen significantly smaller than the size of thediffraction patterns, no additional usable information is gained.

Regarding the choice of the lens size it should be noted that there is atradeoff between the size of the diffraction patterns and the achievableDOF. The smaller a lens is chosen, the larger its diffraction patternand the better its DOF. It is important to note, however, that there isa degree of freedom in the choice of the lens size in order to achievethe best compromise between resolution and DOF of a specificapplication. In coded aperture imaging, however, this degree of freedomdoes not exist. Rather, in coded aperture imaging the sensor pixel sizeand aperture element size are constrained to be more or less identical.

Camera Sensor and Sensor Output Adjustments

According to one embodiment, the sensor 504 of FIG. 5 is a CCD sensor.More specifically, a color CCD sensor using a color filter array(“CFA”), also know as a Bayer pattern, is used for color imaging. A CFAis a mosaic pattern of red, green and blue color filters placed in frontof each sensor pixel, allowing it to read out three color planes (atreduced spatial resolution compared to a monochrome CCD sensor). FIG. 9illustrates an exemplary RGB Bayer Pattern. Each pixel cluster 900consists of 4 pixels 901-904, with color filters over each pixel in thecolor of (G)reen, (R)ed, or (B)lue. Note that each pixel cluster in aBayer pattern has 2 Green pixels (901 and 904), 1 Red (902) and 1 Blue(903). Pixel Clusters are typically packed together in an array 905 thatmakes up the entire CFA. It should be noted, however, that theunderlying principles of the invention are not limited to a Bayerpattern.

In an alternative embodiment, a multi-layer color image sensor is used.Color sensors can be implemented without color filters by exploiting thefact that subsequent layers in the semiconductor material of the imagesensor absorb light at different frequencies while transmitting light atother frequencies. For example, Foveon, Inc. of Santa Clara, Calif.offers “Foveon X3” image sensors with this multi-layer structure. Thisis illustrated in FIG. 10 in which semiconductor layer 1001 is an arrayof blue-sensitive pixels, layer 1002 is an array of green-sensitivepixels, and layer 1003 is an array of red-sensitive pixels. Signals canbe read out from these layers individually, thereby capturing differentcolor planes. This method has the advantage of not having any spatialdisplacement between the color planes. For example, pixels 1011-1013 aredirectly on top of one another and the red, green and blue values haveno spatial displacement between them horizontally or vertically.

According to one embodiment of the present invention, each of the 3 RGBcolor planes are read out from a color imaging sensor (CFA ormulti-layer) and are reconstructed individually. In one embodiment, thereconstruction algorithms detailed below are applied individually toeach of the 3 color planes, yielding 3 separate color planes of thereconstructed image. These can then be combined into a single RGB colorimage.

As illustrated in FIG. 11 a, the analog output signal of imaging sensor1101 is digitized by an analog-to-digital converter (A/D) 1104 in orderto allow digital image reconstruction and post-processing. In order toexploit the full dynamic range of the A/D 1104, the sensor output isfirst amplified by an op amp 1100 before feeding it into the A/D. The opamp 1100 applies a constant zero offset z (1102) and a gain g (1103) tothe image sensor 1101 output signal. The input signal to the A/D 1104 iss′=g (s−z) where s is the image sensor 1101 output signal. In oneembodiment, offset 1102 and gain 1103 are chosen in such a way that thefull dynamic range of the A/D 1104 is exploited, i.e., that the lowestpossible sensor signal value s_(min) corresponds to zero and the highestpossible sensor signal value s_(max) corresponds to the maximum allowedinput signal of the A/D 1104 without the A/D 1104 going into saturation.

FIG. 12 depicts the characteristic of the resulting system. Note that asdescribed above, the dynamic range of the scene is compressed by codedlens imaging; therefore, zero offset and gain may be higher than inconventional imaging with a single lens. In one embodiment, zero offsetand gain are automatically chosen in an optimal fashion by the codedlens camera according to the following set of operations, illustrated inthe flowchart in FIG. 11 b:

At 1110, an initial zero offset is selected as the maximum possible zerooffset and a relatively large initial step size is selected for the zerooffset. At 1111 an initial gain is selected as the maximum possible gainand a relatively large initial step size is selected for the gain.

At 1112, an image is acquired using the current settings and adetermination is made at 1113 as to whether there are any pixels in theA/D output with a zero value. If there are pixels with a zero value,then the current zero offset step size is subtracted from the currentzero offset at 1114 and the process returns to 1112.

Otherwise, if there are no pixels with a zero value, a check is made at1115 as to whether the current zero offset step size is the minimumpossible step size. If this is not the case, then at 1116 a, the currentzero offset step size is added to the current zero offset, making surethat the maximum possible zero offset is not exceeded. The current zerooffset step size is then decreased at 1116 b (e.g., by dividing it by10) and the process returns to 1112.

Otherwise, at step 1117, an image is acquired using the currentsettings. At 1118, a determination is made as to whether there are anypixels in the A/D output with the maximum output value (e.g. 255 for an8-bit A/D). If there are pixels with the maximum value, then the currentgain step size is subtracted from the current gain at 1119 and theprocess returns to 1117.

Otherwise, at 1120, a determination is made as to whether the currentgain step size is the minimum possible step size. If this is not thecase, then at 1121 a, the current gain step size is added to the currentgain, making sure the maximum possible gain is not exceeded. The currentgain step size is then decreased at 1121 b (e.g., by dividing it by 10)and the process returns to 1117. Otherwise, the process ends with thecurrent zero offset and gain settings.

Before applying the reconstruction algorithm, the effects of zero offsetand gain have to be reversed. In one embodiment, this is done bydigitally computing the corrected sensor signal s* from the A/D outputsignal s″ whereas s″ is the output of the A/D pertaining to the A/Dinput signal s′ and s*=s″/g+z. Note that in the absence of noise in theop amp 1100 and in the absence of quantization errors, s* would equalthe original analog sensor output signal s.

In coded lens imaging, each sensor pixel is exposed to light emitted bydifferent pixels of the scene, reaching the sensor pixel throughdifferent lenses within the coded lens array. The reconstructionalgorithms used in coded lens imaging assume that sensor image is thelinear sum of all sensor images which each individual lens would haveprojected onto the sensor. Therefore, in one embodiment, the sensoroutput signal s is an exactly linear function of the number p of photonshitting each sensor pixel during the exposure time. The functiondescribing the dependency of the sensor output signal from the actualphoton count of each sensor pixel is called the “transfercharacteristic” of the sensor. CCD imaging sensors have a lineartransfer characteristic over a large range of intensities while CMOSimaging sensors have a logarithmic transfer characteristic. A graphshowing typical CMOS and CCD image sensor transfer characteristics isshown in FIG. 13. When the transfer characteristic s=f(p) of the sensoris known, it can be compensated for by means of a lookup table. That is,instead of using the value s* for the reconstruction, the value LUT(s*)=LUT (s″/g+z) is used where LUT is a lookup table compensating forany non-linear effects in the sensor transfer characteristic. Once theoperations above have been completed, the adjusted sensor image isstored in the memory of the DSP, ASIC or other type of imagereconstruction processor 530 of the camera in preparation for imagereconstruction.

It should be noted that in coded lens photography, the dynamic range ofthe sensor signal may be different from the dynamic range of the imagedscene. Since each sensor pixel is exposed to multiple scene pixelsacross the entire FOV, the coded lens array has an averaging effect onthe range of intensities. Even scenes with a high dynamic range (e.g.dark foreground objects and bright background objects) produce sensorsignals with a lower dynamic range. In the process of imagereconstruction, the dynamic range of the original scene is reconstructedindependently of the dynamic range of the imaging sensor. Rather, thelimited dynamic range of the imaging sensor (finite number of bits forquantization) leads to quantization errors which can be modeled as noisein the sensor image. This quantization noise also causes noise in thereconstruction. The noise is more prominent close to the edges of thereconstructed image as described above, since in these areas a highmultiplier must be applied for compensating for baffle attenuation. As aresult, imaging a scene with high dynamic intensity range with animaging sensor with low dynamic range causes the reconstructed image tobe more noisy, but not to have lower dynamic range. This is in contrastto conventional single lens photography where the dynamic range of theimaging sensor directly limits the maximum dynamic range of the scenewhich can be imaged.

Scene Reconstruction

The following set of operations are used in one embodiment of theinvention to reconstruct scenes from sensor images that are captured andadjusted as described above. According to Gottesman, a MURA lens arrayis constructed in the following way. First consider a Legendre sequenceof length p where p is an odd prime. The Legendre sequence l (i) wherei=0, 1, . . . , p−1 is defined as:

l(0)=0,

l(i)=+1 if for any k=1, 2, . . . , p−1 the relation k² mod p=l issatisfied

l(i)=−1 otherwise.

Then the MURA a (i, j) of size p×p is given by:

a(0,j)=0 for j=0, 1, . . . , p−1,

a(i, 0)=1 for i=1, 2, . . . , p−1,

a(i, j)=(l(i)*l(j)+1)/2 for i=1, 2, . . . , p−1 and j=1, 2, . . . , p−1.

In this MURA array, a 1 represents a lens and a 0 represents an opaqueelement in the coded lens array. The number of lenses in a single periodof this MURA is K=(p²−1)/2. The periodic inverse filter g (i, j)pertaining to this MURA is given by:

g(0,0)=+1/K,

g(i,j)=(2a(i,j)−1)/K if i>0 or j>0.

It can be shown that the periodic cross-correlation function phi (n, m)between a (i, j) and g (i, j) is 1 for n=0 and m=0, and 0 otherwise. Theperiodic inverse filter pertaining to a MURA therefore has the samestructure as the MURA itself, except for a constant offset and constantscaling factor, and for the exception of a single element which isinverted with respect to the original MURA. FIG. 2 shows various sizesof MURA lens array patterns.

In a similar manner, a PBA according to Busboom can be used as a lensarray. Its periodic inverse filter has exactly the same structure as thePBA itself, except for a constant offset and constant scaling factor.The formulas and algorithms for generating PBAs can be found in A.BUSBOOM: ARRAYS UND REKONSTRUKTIONSALGORITHMEN FUER BILDGEBENDE SYSTEMEMIT CODIERTER APERTUR. VDI VERLAG, DUESSELDORF, 1999, ISBN3-18-357210-9, PAGES 52-56. PBAs of order 8 and 24 are illustrated inFIG. 2. They are enlarged relative to the MURA patterns.

When an object at a constant distance is imaged with a coded lens array,the sensor image is given by the periodic cross-correlation function ofthe object function with the coded lens array, magnified by a geometricmagnification factor f as described above. For reconstructing theoriginal object, the periodic cross-correlation function of the measuredsensor image with an appropriately magnified version of the periodicinverse filter is computed. In the absence of noise and otherinaccuracies of the measured sensor image, the result equals theoriginal object function.

Performing the inverse filtering then consists of the following set ofoperations:

1. Compute the periodic inverse filter pertaining to the coded lensarray pattern.2. Compute a geometrically magnified version of this inverse filter insuch a way that the distance between two adjacent elements of theinverse filter equals the separation of two adjacent lens projections ofthe scene in the sensor plane. The magnified version of the inversefilter is resampled according to the sensor resolution in such a waythat all values between two filter elements are padded with zeros andthe filter elements are represented as non-zeros peaks, each having thesize of a single pixel. According to one embodiment of the invention, ifthe distance between two adjacent lens projections is not an integermultiple of the pixel size, standard interpolation techniques known fromsignal processing are used in order to compute the magnified version ofthe inverse filter. In this case, each filter element may spread acrossmore than one pixel. It should be noted that the separation between twoadjacent lens projections varies with the distance of the object fromthe coded lens camera. Therefore, different inverse filters may be usedin order to reconstruct objects at different distances.3. Compute the two-dimensional, periodic cross-correlation functionbetween the sensor image and the inverse filter, resampled to the sensorresolution according to step (2).4. Divide each pixel of the result of 3. by K, the number of lenses in asingle period of the MURA or PBA or other lens array pattern.

Reconstruction of a Scene with One Object at a Known Range

As mentioned above, in one embodiment, reconstruction of the scene fromthe sensor signal is performed in a digital signal processor (“DSP”)(e.g., DSP 132) integrated into the camera or in a computing deviceexternal to the camera. In one embodiment, scene reconstruction consistsof the following sequence of operations:

1. Linearize the transfer characteristic of the output signal of thesensor such that the linearized output signal of each sensor pixel isproportional to the number of photons counted by the sensor pixel.2. Periodically cross-correlate the sensor signal with the appropriatelymagnified periodic inverse filter pertaining to the coded lens array.3. Clip the result to non-negative pixel values.4. Compensate for baffle attenuation by multiplying each pixel with anappropriate amplification factor.5. Optionally smooth the off-axis parts of the result which are moresubject to noise amplification during (4) than the center part of theresult.

It should be noted that if the aperture array is a MURA, the inversefiltering of operation (2) can be decomposed into a sequence of twoone-dimensional filter operations, one of which is applied per image rowand the other of which is applied per image column. This decompositionmay reduce the computational complexity of (2) in the case of largearray orders.

FIG. 17 a illustrates three examples of the projection andreconstruction of three flat scenes at a known range using the proceduredescribed in the preceding paragraph. In the example, a 3×3 MURA patternwas used for the lens array (1700). The distance (pitch) between twoadjacent lenses in the array was 3 mm. Each lens had a focal length of 5mm which was also the distance between the lens array and the sensor.The sensor was a 10×10 mm sensor with 30×30 um square pixels. Scene 1701is a flat (2-dimensional) test pattern of 307×307 pixels. It isprojected through the 3×3 element MURA lens array 1700 onto the imagesensor, resulting in the sensor image 1711. Sensor image 1711 isadjusted and reconstructed per the process described above resulting inreconstruction 1721. Note that the extreme corners 1730 ofreconstruction 1721 are not accurately reconstructed. This is due to theattenuation of light during the projection through the baffles at theextreme edges of the image. In the same manner, flat 307×307 pixel image1702 is projected through the lens array 1700 resulting in sensor image1712 and is processed to result in reconstruction 1722. In the samemanner, flat 307×307 pixel image 1703 is projected through the lensarray 1700 resulting in sensor image 1713 and is processed to result inreconstruction 1723.

FIG. 17 b illustrates three similar examples as FIG. 17 a. However, inFIG. 17 b a 24×24 PBA pattern was used as the lens array pattern (1750).The lenses had a pitch of 0.39 mm such that the total size of the lensarray was similar to that of FIG. 17 a (18.72×18.72 mm in FIG. 17 b and18×18 mm in FIG. 17 a). The same sensor as in the example of FIG. 17 awas used. The lenses had again a focal length of 5 mm. Scene 1701 isprojected through the 24×24 element PBA lens array 1750 onto the imagesensor, resulting in the sensor image 1731. Sensor image 1731 isadjusted and reconstructed per the process described above resulting inreconstruction 1741. In the same manner, flat 307×307 pixel image 1702is projected through the lens array 1750 resulting in sensor image 1732and is processed to result in reconstruction 1742. In the same manner,flat 307×307 pixel image 1703 is projected through the lens array 1750resulting in sensor image 1733 and is processed to result inreconstruction 1743. It can be observed from the sensor images(1711-1713 and 1731-1733) in the two examples that increasing the orderof the lens array flattens the contrast in the sensor image. In thesensor images 1731-1733 of FIG. 17 b, no more details of the originalscene are recognizable. However, as can be seen from the reconstructions1741-1743, the sensor images still contain all the information necessaryfor reconstructing the original scene.

It is noted that, as described above, sensor images 1711-1713 and1731-1733 may be quantized at a given number of bits per pixel (e.g. 8),but may yield in the reconstructed images 1721-1723 and 1741-1743 animage with a useful dynamic range comparable to a higher number of bitsper pixel (e.g. 10).

Reconstruction of a Scene with One Object at an Unknown Range

In one embodiment, operation (2) of the sequence of operations describedabove in section “Reconstruction of a Scene with One Object at a KnownRange” are repeated for different expected object ranges o, when thetrue object range is uncertain or unknown. By this technique a set ofmultiple reconstructions is obtained from the same sensor signal. Withinthis set of reconstructions, the one where the expected object range isidentical with or closest to the true object range will be the mostaccurate reconstruction of the real scene, while those reconstructionswith a mismatch between expected and true range will contain artifacts.These artifacts will be visible in the reconstruction as high-frequencyartifacts, such as patterns of horizontal or vertical lines or ringingartifacts in the neighborhood of edges within the reconstruction.

According to one embodiment of the present invention, among this set ofreconstructions, the one with the least artifacts is manually orautomatically selected. This allows a change in the range ofreconstruction without the need to pre-focus the camera and, inparticular, without the need to mechanically move parts of the camera,as would be required with a conventional single lens camera, or topre-select an expected object range. Further, this allows the user todecide about the desired range of reconstruction after the imageacquisition (i.e. retrospectively). Preferably, the range ofreconstruction is automatically selected from the set of reconstructionsby identifying the reconstruction with the least amount ofhigh-frequency artifacts and the smoothest intensity profile.

A simple, but highly effective criterion for “focusing” a coded lenscamera, i.e., for determining the correct range from a set ofreconstructions, is to compute the mean m and the standard deviation σof all gray level values of each reconstruction. Further, the ratio m/σis computed for each reconstruction. The reconstruction for which thisratio takes on its maximum is chosen as the optimal reconstruction,i.e., as the reconstruction which is “in focus.” This technique producesthe best results if the objects in the scene are in focus in each of theindividual projections.

FIG. 18 illustrates how a scene is reconstructed at a set of differentranges. A similar system configuration as in FIG. 17 b was used forproducing FIG. 18, i.e. a 24×24 PBA pattern was used for projection. Theoriginal scene was the test image 1701 from FIG. 17 b which was imagedat a range of 1,000 mm. Reconstructions were computed from the resultingsensor image at assumed ranges of 500 mm (1801), 800 mm (1802), 1,000 mm(1803) and 5,000 mm (1804). In the figure, it can clearly be seen thatthe reconstruction in the lower left-hand corner at the correct range of1,000 mm looks “clean” while the reconstructions at different rangescontain strong high-frequency artifacts. FIG. 18 also shows the standarddeviation (“stddev”) of the gray values in each of the fourreconstructions. FIG. 18 further shows the quotients (m/s) of the grayvalue mean, divided by the gray value standard deviation, for each ofthe four reconstructions. This value starts at 0.0977 at an assumedrange of 500 mm, then continuously increases to a maximum of 2.0 at thecorrect range of 1,000 mm, then continuously decreases, reaching a valueof 0.1075 at an assumed range of 5,000 mm. The example shows how thetrue range of the scene can be easily computed from a set ofreconstructions by choosing the reconstruction at which the quotient m/stakes on its maximum.

Optimization of Reconstruction of a Scene with One Object at an UnknownRange

According to one embodiment, only a partial reconstruction of parts ofthe image is computed using different expected object ranges o. Apartial reconstruction is computed by only evaluating the periodiccross-correlation function in operation (2) above in section“Reconstruction of a Scene with One Object at a Known Range” for asubset of all pixels of the reconstructed image, thus reducing thecomputational complexity of the reconstruction. This subset of pixelsmay be a sub-sampled version of the image, a contiguous region of theimage, or other suitable subsets of pixels. Then, the twoone-dimensional periodic filtering operations only need to be evaluatedfor a subset of rows and/or columns of the reconstructed image. From theset of partial reconstructions, the one with the least amount ofhigh-frequency artifacts and the smoothest intensity profile isidentified in order to determine the true object range o. For theidentified true object range o, a full reconstruction is then performed.This way, the computational complexity of reconstructing the scene whileautomatically determining the true object range o can be reduced.

Reconstruction of a Scene with Multiple Objects at Unknown Ranges

According to one embodiment, a set of full image reconstructions atdifferent object ranges o is computed. Since objects in different partsof the scene may be at different ranges, the reconstructions aredecomposed into several regions. For each region, the object range owhich yields the least amount of high-frequency artifacts and thesmoothest intensity profile is identified. The final reconstruction isthen assembled region by region whereas for each region thereconstruction with the optimum object range o is selected. This way,images with infinite depth of FOV (from close-up to infinity) can bereconstructed from a single sensor signal.

The combined reconstruction is of lower quality than a flatreconstruction of a flat scene, i.e., of a scene with only a singleobject at a single range. The presence of other regions in the scenewhich are “out of focus” do not only cause the out-of-focus regions tobe of inferior quality in the reconstruction, but also cause thein-focus region to contain artifacts in the reconstruction. In otherwords, there is a “crosstalk” between the out-of-focus and the in-focusregions. This crosstalk and techniques for suppressing it are addressedin the following.

Reduction of “Crosstalk” in Reconstructing a Scene with Multiple Objectsat Unknown Ranges

As explained before, the “flat” reconstruction of a region r₁ at rangeo₁ would only be accurate if the entire scene were at a constant rangeo₁. If, however, other regions are at different ranges, there will be“crosstalk” affecting the reconstruction of region r₁. Therefore,according to one embodiment, an iterative reconstruction procedure isemployed which eliminates this crosstalk among different regions in thescene at different ranges. The iterative reconstruction procedureaccording to one embodiment of the invention consists of the followingset of operations.

1. Computing a “flat” reconstruction, i.e., a reconstruction assuming ahomogeneous range across the entire scene, at a set of ranges o₁, o₂, .. . , o_(n).2. Using the flat reconstructions obtained this way to decompose thescene into a number of contiguous regions r₁, r₂, . . . , r_(m) andcorresponding ranges o₁, o₂, . . . , o_(m). The decomposition is done insuch a way that for each region its reconstruction r_(i) at range o_(i)is “better”, i.e., contains less high-frequency artifacts and has asmoother intensity profile, than all reconstructions of the same regionat other ranges.3. For each of the reconstructed regions r_(i) (i=1, 2, . . . , m)computing its contribution s_(i) to the sensor image. This is done bycomputing the two-dimensional, periodic cross-correlation function ofr_(i) with the lens array pattern. Note that if the reconstructions ofall the regions were perfect, then the sum of all sensor imagecontributions would equal the measured sensor image s.4. For each of the reconstructed regions r_(i) (i=1, 2, . . . , m)subtracting the sensor image contributions of all other regions from themeasured sensor image, i.e.,

${\Delta \; s_{i}} = {s - {\sum\limits_{k \neq i}s_{k}}}$

Note that each Δs_(i) (i=1, 2, . . . , m) now contains a sensor imagepertaining only to region r_(i), the contributions of all other regionsr_(i), j≠i, being mostly suppressed. Due to the fact that thereconstruction of the other regions will not be perfect but containreconstruction errors, there will be some remaining crosstalk, i.e. theΔs_(i) will contain some residual contributions from the other regions.However, this crosstalk is much lower than the crosstalk withoutcomputation of a difference sensor image.5. Utilizing the Δs_(i) (i=1, 2, . . . , m) to compute a refinedreconstruction r′_(i) for each region at range o_(i). Optionally, thisstep can be repeated with a number of different ranges around theinitial range o_(j) in order to also refine the range estimate o_(i). Inthis case, for each region the reconstruction and range with the leasthigh-frequency artifacts and the smoothest intensity profile areselected.6. Optionally, going back to operation (3) for an additional refinementof each region.

Determination of Range of Objects within a Reconstructed Scene

According to one embodiment, the output signal of the coded lens camera(in addition to the two-dimensional image information) also containsrange information for each image pixel or for several image regions, asdetermined from finding the object range o for each region with theleast amount of high-frequency artifacts and the smoothest intensityprofile. Thus, for every pixel reconstructed in the image, in additionto the reconstruction deriving a single intensity value (for grayscalevisible light, infrared, ultraviolet or other single frequencyradiation) or three intensity values for visible red, green, blue colorlight, the reconstruction assigns a z value indicating the distance fromthe camera to the object at that pixel position in the image. This way,three-dimensional image data can be obtained from a single,two-dimensional sensor signal. Further, the range data allows thecamera, an external imaging manipulation system, or the user, utilizingan image manipulation application or system to easily segment thetwo-dimensional image into different regions pertaining to differentparts of the scene, such as separating objects in the foreground of ascene from the background of a scene.

Using Range Information to Eliminate the Need for Blue/Green Screens

Chroma-keying is a technique commonly used in video and photographicproduction to separate a foreground image from a solid background color.Typically, a “blue screen” or “green screen” is used, which is a verycarefully colored and illuminated screen that is placed behind aperformer or object while the scene is photographed or captured on videoor film. Either in real-time or through post-processing, a hardware orsoftware system separates the presumably distinctively coloredforeground image from the fairly uniformly colored background image, sothat the foreground image can be composited into a different scene. Forexample, typically the weatherperson on a TV news show is chroma-keyedagainst a blue or green screen, then composited on top of a weather map.

Such blue or green screens are quite inconvenient for production. Theyare large and bulky, they require careful illumination and must be keptvery clean, and they must be placed far enough behind the foregroundobject so as not to create “backwash” of blue or green light onto theedges of the foreground object. Utilizing the principles of theembodiment of the previous paragraph, an image can be captured without ablue or green screen, and the z value provided with each pixel willprovide a compositing system with enough information to separate aforeground object from its background (i.e., by identifying which pixelsin the scene contain the image of closer objects and should be preservedin the final image, and which pixels in the scene contain the image offurther away objects and should be removed from the final image). Thiswould be of substantial benefit in many applications, includingphotographic, video, and motion picture production, as well as consumerapplications (e.g. separating family members in various pictures fromthe background of each picture so they may be composited into a grouppicture with several family members).

FIG. 20 shows how a person 1901 from FIG. 19 can readily be placed in ascene with a different background, such as the castle 2002 with thebackground mountains 2002 removed from the picture. This is simplyaccomplished by replacing every pixel in the image reconstructed fromFIG. 19 that has a z value greater than that of person 1901 with a pixelfrom the image of the castle 2002. Once again, the processing of zvalues may be implemented using virtually any type of image processorincluding, for example, a DSP, ASIC or a general purpose processor.

Using Range Information to Improve Optical Motion Capture Systems

The per-pixel distance ranging capability of one embodiment also hasapplications in optical performance motion capture (“mocap”). Mocap iscurrently used to capture the motion of humans, animals and props forcomputer-generated animation, including video games (e.g. NBA Live 2005from Electronic Arts of Redwood City, Calif.), and motion pictures (e.g.“The Polar Express”, released by the Castle Rock Entertainment, adivision of Time Warner, Inc, New York, N.Y.). Such mocap systems (e.g.those manufactured by Vicon Motion Systems, Ltd. of Oxford, UnitedKingdom) typically utilize a number of single lens video camerassurrounding a performance stage. Retroreflective markers (or otherdistinctive markings) are placed all over the bodies of performers andupon props. The video cameras simultaneously capture images of themarkers, each capturing the markers within its FOV that is notobstructed. Finally, software analyzes all of the video frames and bytriangulation, tries to identify the position of each marker in 3Dspace.

FIG. 21 is a photograph of an exemplary motion capture session. Thethree bright rings of light are rings of LEDs around the single lensesof the video cameras 2101-2103. The performers are wearing tight-fittingblack suits. The gray dots on the suits are retroreflective markers thatreflect the red LED light back to the camera lenses causing the markersto stand out brightly relative to the surrounding environment. Four suchretroreflective markers on the knees of the left performer areidentified as 2111-2114.

Because all of the markers look the same in a camera image, one of thechallenges faced by mocap systems is determining which marker imagecorresponds to which marker (or markers) in the scene, and then trackingthem frame-to-frame as the performers or props move. Typically, theperformer stands roughly in a known position, with the markers placed inroughly known positions on the performer's body (or on a prop). Thecameras all capture an initial frame, and the software is able toidentify each marker because of the approximately known position of theperformer and the markers on the performer. As the performer moves, themarkers move in and out of the fields of view of the cameras, and oftenbecome obscured from the one, several or even all cameras as theperformer moves around. This creates ambiguities in the mocap system'sability to continue to identify and track the markers.

For example, if a frame of a given video camera shows a marker centeredat a given (x, y) pixel position, it is quite possible that the image isreally showing two markers lined up one behind the other, leaving onecompletely obscured. In the next frame, the performer's motion mayseparate the markers to different (x, y) positions, but it can bedifficult to determine which marker was the one in front and which wasthe one in back in the previous frame (e.g. the marker further away mayappear slightly smaller, but the size difference may be less than theresolution of the camera can resolve). As another example, a performermay roll on the floor, obscuring all of the markers on one side. Whenthe performer stands up, many markers suddenly appear in a camera'simage and it may be difficult to identify which marker is which. Anumber of algorithms have been developed to improve this markeridentification process, but it is still the case that in a typicalmotion capture session, human operators must “clean up” the captureddata by manually correcting erroneous marker identification,frame-by-frame. Such work is tedious, time-consuming and adds to thecost of mocap production.

In one embodiment of the invention, single lens video cameras arereplaced by video cameras utilizing coded lens techniques describedherein. The coded lens cameras not only capture images of the markers,but they also capture the approximate depth of each marker. Thisimproves the ability of the mocap system to identify markers insuccessive frames of capture. While a single lens camera only providesuseful (x, y) position information of a marker, a coded lens cameraprovides (x, y, z) position information of a marker (as describedabove). For example, if one marker is initially in front of the other,and then in a subsequent frame the markers are separated, it is easy forthe coded lens camera to identify which marker is closer and which isfurther away (i.e., using the z value). This information can then becorrelated with the position of the markers in a previous frame beforeone was obscured behind the other, which identifies which marker iswhich, when both markers come into view.

Additionally, it is sometimes the case that one marker is only visibleby one mocap camera, and it is obscured from all other mocap cameras(e.g. by the body of the performer). With a single lens mocap camera, itis not possible to triangulate with only one camera, and as such themarkers (x, y, z) position can not be calculated. With a coded lenscamera, however, the distance to the marker is known, and as a result,its (x, y, z) position can be easily calculated.

Using Range Information to Improve Robot Vision Systems

In another embodiment, coded lens cameras are used in robot visionsystems. For example, in manufacturing applications a conventional lenscamera can not provide distance information for a robotic armature todetermine the (x, y, z) position of a part that it needs to pick up andinsert in an assembly, but a coded lens camera can.

Using Increased Dynamic Range and (Distance) Range Information toImprove Security Camera Systems

In one embodiment, coded lens cameras are employed within securitysystems. Because they have the ability to use low dynamic range sensorsto capture high dynamic range scenes, they can provide usable imagery insituations where there is backlighting that would normally wash out theimage in a conventional single lens camera. For example, if an intruderis entering a doorway, if there is bright daylight outside the doorway,a conventional single lens camera may not be able to resolve a usefulimage both outside the doorway and inside the doorway, whereas a codedlens camera can.

Embodiments of the invention may include various steps as set forthabove. The steps may be embodied in machine-executable instructionswhich cause a general-purpose or special-purpose processor to performcertain steps. For example, the various operations described above maybe software executed by a personal computer or embedded on a PCI cardwithin a personal computer. Alternatively, or in addition, theoperations may be implemented by a DSP or ASIC. Moreover, variouscomponents which are not relevant to the underlying principles of theinvention such as computer memory, hard drive, input devices, etc, havebeen left out of the figures and description to avoid obscuring thepertinent aspects of the invention.

Elements of the present invention may also be provided as amachine-readable medium for storing the machine-executable instructions.The machine-readable medium may include, but is not limited to, flashmemory, optical disks, CD-ROMs, DVD ROMs, RAMs, EPROMs, EEPROMs,magnetic or optical cards, propagation media or other type ofmachine-readable media suitable for storing electronic instructions. Forexample, the present invention may be downloaded as a computer programwhich may be transferred from a remote computer (e.g., a server) to arequesting computer (e.g., a client) by way of data signals embodied ina carrier wave or other propagation medium via a communication link(e.g., a modem or network connection).

Throughout the foregoing description, for the purposes of explanation,numerous specific details were set forth in order to provide a thoroughunderstanding of the present system and method. It will be apparent,however, to one skilled in the art that the system and method may bepracticed without some of these specific details. For example, while theembodiments of the invention are described above in the context of a“camera,” the underlying principles of the invention may be implementedwithin virtually any type of device including, but not limited to,PDA's, cellular telephones, and notebook computers. Accordingly, thescope and spirit of the present invention should be judged in terms ofthe claims which follow.

1. An apparatus for coding images comprising: a coded lens arrayincluding a plurality of lenses coupled together to form a codedpattern.
 2. The apparatus as in claim 1 further comprising: alight-sensitive semiconductor sensor coupled to the coded lens array andpositioned at a specified distance behind the coded lens array, thelight-sensitive sensor configured to sense light transmitted through thelenses in the coded lens array.
 3. The apparatus as in claim 2 furthercomprising: image reconstruction logic to generate image data using thelight transmitted through the lenses and sensed by the light-sensitivesensor, the image data representing an image of a subject positioned infront of the coded lens array.
 4. The apparatus as in claim 1 whereinthe coded pattern is a Uniformly Redundant Array (URA) pattern.
 5. Theapparatus as in claim 1 wherein the coded pattern is a ModifiedUniformly Redundant Array (MURA) pattern the pattern of claim 1 is aPBA.
 6. The apparatus as in claim 1 wherein the coded pattern is arandom pattern.
 7. The apparatus as in claim 1 wherein there is opaquematerial blocking array elements which do not contain lenses.
 8. Theapparatus as in claim 2 further comprising: an image sensor readoutsubsystem communicatively coupled to receive image data from the lightsensitive semiconductor sensor and to adjust zero offset and/or gain ofpixel values of the image data.
 9. The apparatus as in claim 2 furthercomprising: a plurality of baffles configured between the coded lensarray and the light-sensitive semiconductor sensor to collimate lightpassing between the coded lens array and the light-sensitivesemiconductor sensor.